Problem: Simplify the following expression: $\sqrt{63} + \sqrt{7}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{63} + \sqrt{7}$ $= \sqrt{9 \cdot 7} + \sqrt{7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7} + \sqrt{7}$ $= 3\sqrt{7} + \sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 + 1 )\sqrt{7} = 4\sqrt{7}$